1. Kim's age is four times that of her sister. When you add Kim's age to her sister's age, you get 60. How old is each sister

(a) Write an equation that represents the situation. Explain any variable used.

(c) Solve the equation from Part (a). Show your work. State your solution as a complete sentence.

a) Let us assume Kim's sister age = x years.

Kim's age is four times of her sister's age.

4 times of x = 4*x = 4x.

Sum of Kim's age and Her sister's age = 60.

So, we can setup an equation

Kim's age + Sister's age = 60

4x + x = 60.

So, the equation for the situation would be 4x+x = 60, where x is the age taken for Kism's sister.

b) We have 4x+x = 60.

First we will combine like terms

4x and x are like terms.

On adding 4x and x, we get 5x.

Therefore, the equation would become

5x = 60.

We are solving eqation for x.

So, dividing both sides by 5, we get

5x/5 = 60/5

x = 12.

Therefore, sister's age is 12 years and Kim's age is 4 times of it, that is 4*12 = 48 years.